what is the y-intercept for y = 6x + 2

(a) The likelihood function for this sample is given by:

L(λ) = λ^2 * exp(-λ * (5 + 3 + x))

where x is the third observation, X₃, which is larger than 10.

(b) To find the MLE for λ, we take the derivative of the log-likelihood with respect to λ and set it equal to zero:

d/dλ ln(L(λ)) = 2/λ - (5 + 3 + x) = 0

Solving for λ, we find that the MLE for λ is λ = (2) / (5 + 3 + x).

Since x is greater than 10, the MLE for λ is positive and less than 2/(5 + 3 + 10) = 2/18

Therefore, the correct answer is as given above

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Answer:

12.96

Step-by-step explanation:

13 members are missing today.

You can calculate this by subtracting the percentage of members present (81%) from 100% and then multiplying that number by the total number of team members (16).

100-81 = 19

19/100*16 = 3.04

16-3.04 = 12.96 = 13 (rounded)

Answer:

3 members MISSING

Step-by-step explanation:

0.81 x 16 = ~13

16 - 13 = 3 missing members

The limit of x + x2 divided by 1 - 4x2 as x approaches infinity is 0. To solve this limit, we can use l'Hospital's Rule.

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Answer:

The exterior of a triangle is the sum of two of its interior angles except the one adjacent to it. The angle x is evaluated as 135°.

What is a triangle?

A triangle is a two dimensional shape bounded by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.

Given that,

There is a triangle shown in the figure with following angles,

∠y = 102°  and ∠Z = 57°.

Angle x is the exterior angle of the given triangle. Use the property of exterior angle to get,

∠x  = ∠B + ∠Z

    = (180° - y) + 57°

    = (180° - 102°) + 57°

    = 135°

Hence, the angle x has been worked out as ∠x = 135°.

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The Constant of proportionality is [tex]\frac{1}{2}[/tex].

What is constant of proportionality?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Here to find constant of proportionality we need to divide y by x. Then,

=> constant of proportionality = [tex]\frac{y}{x}[/tex]

Here put x=10 and y=5 then

=> [tex]\frac{5}{10} = \frac{1}{2}[/tex]

Now put x=20 and y=10 then

=> [tex]\frac{10}{20} = \frac{1}{2}[/tex]

Hence the constant of the proportionality is [tex]\frac{1}{2}[/tex].

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Answer: she will save 40$

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Operation sign between two of the digits is 96 ÷ 2 × 5 + 8 × 0 - 7 = 8,818

This question uses the Order of Operations (PEMDAS) theory.

The order of operations states that we should work through equations in the following order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In this question, the first operation was division (96 ÷ 2), followed by multiplication (48 × 5), then addition (240 + 8), then multiplication (248 × 0), and finally subtraction (0 - 7).

Step 1: 96 ÷ 2 = 48

Step 2: 48 × 5 = 240

Step 3: 240 + 8 = 248

Step 4: 248 × 0 = 0

Step 5: 0 - 7 = -7

Step 6: -7 = 8,818

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As a result, the third side's length might be any value higher than 0 and less than 12, or any number bigger than 12 and less than 24.

Hence, option (c) is correct choice.

The length of a triangle's third side must meet the triangle inequality theorem, which says that the total of the lengths of the triangle's two sides must be higher than the length of the triangle's third side.

As a result, the length of the third side of a triangle with two sides of length 12 must be between 0 and 24, omitting 12.

The third side can have the following lengths:

0 < length < 12

12 < length < 24

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The missing option may be:

(a)  6 < length < 12

(b) 2 < length < 4

(c) 12 < length < 24

(d) 15 < length < 30

Answer:

you would be able to pull out $1,933.33 each month for 20 years if you have $400,000 saved for retirement and it earns 7% interest.

The number of miles the business person can travel with 110 dollars is 290 miles.

Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day.

Therefore, the number of miles the business person can travel on 110 dollars can be calculated as follows;

Using equations,

Therefore,

y = 0.25x + 37.33

where

Therefore, let's find the distance he can travel for 110 dollars.

110 = 0.25x + 37.33

110 - 37.33 = 0.25x

72.67 = 0.25x

x = 72.67 / 0.25

x = 290.68

Therefore,

number of miles he can travel = 290 miles

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The function with the greater rate of change will have the greater output value for every input value which is true.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

Let m₁ > m₂ and c₁ > c₂. Then the equations are given as,

y = m₁x + c₁

y = m₂x + c₂

The function with the greater rate of change will have the greater output value for every input value which is true.

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The productivity rate in labor hours per foot for carpenter is 0.062 hour / feet.

In mathematics, a fraction is referred to as a portion of a whole. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.

For carpenter, the total hours contributed are:

(2)(8) = 16 hours

No of das worked by carpenter are 2 days.

The total hours contributed by 2 carpenters are:

16 (2) = 32 hours

The production rate of carpenter is = hours / total work

= 32/ 515 = 0.062 hour / feet.

Hence, the productivity rate in labor hours per foot for carpenter is 0.062 hour / feet.

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The required width and length of the given rectangle is 25/12 cm and 63 / 12 cm.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,
Length = 3 1/6 + width

perimeter of the rectangle = 2[length + width]

15 1/3 = 2 [3 1/6 + width + width]
46/3  × 1/2 =  19/6 + 2 width
23 / 3 - 19 / 6 = 2 width
[46 - 19]/ 12 = width
width = 25/12 cm

Now,
Length = 25/12 + 19/6
Length = 63 / 12 cm

Thus, the required width and length of the given rectangle is 25/12 cm and 63 / 12 cm.

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Answer: -8<x> 2

Step-by-step explanation:

open circles indicate that the number shown is not included therefore x must lie in-between -8 and 2

12 inches is equal to one foot. 12 inches seems like more because 12>1, but they are really equal.

The measure of the angle MNO is 79 degrees

The midpoint of KM and O is also the midpoint of LM as expressed in the information given.

We have the parameters;

Note that the midpoint of the triangle is expressed as;

m/MKL = m/MNO

Now, substitute the values, we get;

61 + 9x = 2x + 75

collect like terms

9x - 2x = 75 - 61

add or subtract the like terms

7x = 14

Now, divide both sides by the coefficient of x, we get;

7x/7 = 14/7

Divide the values

x = 2

Substitute the value into the expression

m/MNO = 2x + 75

m/MNO = 2(2) + 75

expand the bracket

m/MNO = 79

Hence, the value is 79

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The rule for the translation is  (x, y) Right-arrow (x + 2, y – 3).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Given;

A triangle has coordinates F(−2, 3), G(−4, 1), and H(−2, −2)

. The triangle is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5).

If a point A(x, y) is translated a units right and b units down, the new point is at A'(x + a, y - b)

Therefore, the translation of FGH to F'G'H' will be (x + y) ⇒ (x + 2, y - 3).

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Approximately 68% of housing prices are between a low price of $144,000 and a high price of $160,000.

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Given that the mean of housing prices is $152,000 and the standard deviation is $8,000, we can use the Empirical Rule to determine that approximately 68% of housing prices fall within one standard deviation of the mean. This means that the range of prices that contains 68% of the data is between:

$152,000 - $8,000 = $144,000 and $152,000 + $8,000 = $160,000.

So, approximately 68% of housing prices are between a low price of $144,000 and a high price of $160,000.

For the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).

Given is that a point is rotated 90 degrees about the origin.

Assume the point to be -

P(x, y)

For the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).

Therefore, for the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).

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The probability of getting someone who is a woman or a heavy drinker is,

0.546 to three decimal places.

None of the above is the correct option.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given:

The table lists the drinking habits of a group of college students.

If a student is chosen at random,

then the probability of getting someone who is a woman or a heavy drinker,

=P(woman) + P(heavy drinker) - P(woman and heavy drinker)

= 216/405 + 13/405 - 8/405

= 221/405

= 0.546 to three decimal places.

Therefore, the probability is 0.546.

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When dividing two exponential functions with the same base, the second law states that the exponents must be subtracted

f(4) = (6)⁴ = 1296

According to the first law, adding the exponents will multiply two exponential functions with the same base. According to the second law, we must subtract the exponents when dividing two exponential functions with the same base. The third law indicates that we must multiply the exponents in order to increase a power to a new power.

Here,

Given :

=>f(2) = 36

=> f(3) = 216

So,

=> f(x) = (6)ˣ

=>f(4) = (6)⁴ = 1296

If f(x) = , where b > 0 and b 1, is the formula for an exponential function. B is referred to as the base and x is referred to as the exponent, just like in any exponential expression. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by two folds per hour.

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For, the given differential equation, 1) For  800 < P < 10000, the population will increase and 2) For 0 < P < 800, the population will decrease.

                               dP/dt = kP (1- (P/K)) (1-(m/P))   -(1)

where k is a constant and K is the carrying capacity.

Here, K = 10000, m = 800 and k = 0.05

Putting these values in Equation 1 we get,

                      dP/dt = 0.05P (1- (P/10000)) (1-(800/P))

1.) If dP/dt > 0 then P is increasing

As dP/dt > 0

So, 0.05P (1- (P/10000)) (1-(800/P)) > 0

Both ((10000- P)/10000) > 0 and ((P-800)/P) > 0

=> P < 10000 and P > 800

So, for  800 < P < 10000, the population will increase.

2.)  If dP/dt < 0 then P is decreasing

As dP/dt < 0

So, 0.05P (1- (P/10000)) (1-(800/P)) < 0

Both ((10000- P)/10000) > 0 and ((P-800)/P) > 0

=> P > 10000 and P < 800

So, for  0 < P < 800, the population will decrease.

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The least positive integer N such that the set of 1000 consecutive integers beginning with 1000 N is 282.

Let x² appear before 1000N so:

(x+1)² − x² >1000⟹ x ≥ 500

Let A = [1000N, 1000(N+1)]

So I let x=500

then, x²=250000

, obviously this is impossible since the set has a square already.

So now I need to set some number, k² ≥ 5012 = 0 (mod1000)

So I need to solve the quadratic residue:

Lets see: 500²=250000

and 501²=251001

and 502²=252004

501²=500²+1000+ ∑ (12k−1)

502²=500²+2(1000)+∑ (12k−1)

The final answer is: N=282

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.

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.

We know that the sum of angles of a triangle are 180°

If you don't know how to find the angles of a triangle

We use the formula,

[tex](n-2)X180[/tex]

Where n replicates the sides of a polygon

Applying the sides into the formula we get

[tex](3-2)X180\\1X180\\180[/tex]

Now in order to find x we sum up all the angles into a equation

90°+ 65°+ x - 10° = 180°

145 + x = 180

We then transpose 145 to the Right Hand Side (RHS)

x = 180 - 145

x = 35°

Hence , the value of x is 35°

Answer:

x = 127°

x = 36

Step-by-step explanation:

The sum of interior angles for the given geometrical figure is calculated with the following formula:

(s-2) × 180

3 × 180 = 540

90 + 143 + 77 + 103 + x = 540

413 + x = 540

x = 127°

The given is a hexagon. The sum of its exterior angles is equal to 360.

80 + 59 + 2x + 59 + 54 + x = 360

252 + 3x = 360

3x = 108

x = 36

Written without exponents, you'd have

   abbbcc   and    aabbc

Both have one a, two b's, and one c.

The GCF is [tex]ab^2c[/tex], since those are the greatest factors they all have in common.

The slopes I found are (A) equivalent. This means that the slope triangles are (B) similar and no matter what (C) two points I pick on the line the slope will be the (A)same.

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Mathematically, the slope is the change in y divided by the change in x. That is:

Slope = y2-y1 / x2-x1

The slope of the line between points A and B:

A (x1 = -5, y1 = -2) and B (x2 = -2, y2 = 0)

Slope = [(0-(-2) )]/ [-2-(-5)] = 2/3

The slope of the line between points B and C:

B (x1 = -2, y1 = 0) and C (x2 = 4, y2 = 4)

Slope = [4-0]/ [4-(-2)] = 4/6 = 2/3

The slope of the line between points A and C:

A (x1 = -5, y1 = -2) and C (x2 = 4, y2 = 4)

Slope = [(4-(-2))]/ [4-(-5)] = 6/9 = 2/3

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Answer: Negative two times z plus eight.

Step-by-step explanation:

The expression $-2z + 8$ represents "negative two times the quantity of z plus 8". To interpret this as a phrase, we can say "8 increased by the negative of two times the quantity of z."